Differential Encoding over Rayleigh Fading Channels

Abstract-- Multilevel coding and bit-interleaved coded modulation employing differential encoding and non-coherent reception over flat fading channels are assessed. In order to achieve high bandwidth efficiencies mixed amplitude/phase modulation is perform

Performance of Coded Modulation employing Di erential Encoding over Rayleigh Fading ChannelsRobert F.H. Fischer1, Stefano Calabro2, Lutz H.-J. Lampe1, Stefan H. Muller{Weinfurtner1 Corresponding Author: Lutz Lampe Laboratorium fur Nachrichtentechnik, Universitat Erlangen{Nurnberg Cauerstra e 7/NT D{91058 Erlangen, Germany Phone:+49-9131-85-28718, Fax:+49-9131-85-28849 Email: llampe@nt.e-technik.uni-erlangen.deAbstract| Multilevel coding and bit{interleaved coded modulation employing

di erential encoding and non{coherent reception over at fading channels are assessed. In order to achieve high bandwidth e ciencies mixed amplitude/phase modulation is performed. It is shown that multiple symbol detection only provides gains for multilevel coding as Gray labeling of the di erential symbols is not possible.

1 IntroductionCoded modulation schemes for power and bandwidth e cient transmission over the AGWN channel were presented by Ungerbock 1] (trellis{coded modulation (TCM)) and Imai/Hirakawa 2] (multilevel coding (MLC)). Subsequently, TCM was adopted for coherent transmission over at fading channels. A pragmatic approach to coded modulation, called bit{interleaved coded modulation (BICM), was introduced by Zehavi 3]. In many situations, where no coherent reception is possible, it is convenient to use di erential encoding, i.e., to represent information in the transitions between consecutive symbols (e.g. 4]). For high spectral e ciencies, mixed di erential phase/amplitude modulation ((D)APSK) is attractive. In this letter power and bandwidth e cient coded modulation via MLC and BICM employing di erential encoding of APSK on at fading channels are developed and compared. If the underlying channel is slowly time{varying, interleaving and detection1 2

Laboratorium fur Nachrichtentechnik, Universitat Erlangen{Nurnberg, Germany Dipartimento di Ingegneria Elettrica, Universita di Palermo, Italy

Abstract-- Multilevel coding and bit-interleaved coded modulation employing differential encoding and non-coherent reception over flat fading channels are assessed. In order to achieve high bandwidth efficiencies mixed amplitude/phase modulation is perform

can be based on blocks of N 2 symbols. We show that BICM is not well suited for this multiple symbol detection. In contrast to this, properly designed MLC schemes make power and bandwidth e cient digital transmission using di erential encoding over fading channels close to theoretical limits possible.

2 System ModelWe assume transmission over a stationary, slowly time{varying, at Rayleigh fading channel. Channel state and carrier phase o set are expected to be constant over a block of N consecutive symbols. Di erential encoding at the transmitter and di erential detection at the receiver are employed. After (perfect) interleaving based on blocks of length N, a memoryless channel is obtained, given by the at Rayleigh fading model. Details are given in 5]. We employ signal constellations for mixed amplitude/phase modulation, consisting of M= points arranged in distinct concentric rings with radii ri, i= 0; 1;:::;? 1, and uniformly spaced phases ( A PSK). Given the reference symbol (state of the encoder) s= riej'n and N? 1 di erential symbols (a

mplitude and phase increments) a k]= rj k] ej'm k, k= 1;:::; N? 1, the encoder outputs x k]= r(i+j k])mod ej('n+'m k ) . The next state of the di . encoder is then x N? 1]. As coded modulation schemes we assume MLC with multistage decoding (MSD). The rates of the`= (N? 1) log2(M ) binary component codes are designed according to the capacities of the equivalent channels. Here, Ungerbock's labeling (UL) is used. For details and a tutorial review on MLC see 6]. The competitor BICM employs a single binary code with rate equal to the target transmission rate. In case of BICM the di erential symbols are (quasi{)Gray labeled (GL). In each modulation scheme, turbo codes 7] with random interleaver (16 states constituent codes) are used as component codes.]]

3 Simulation ResultsFirst, in Fig. 1 D8PSK using MLC and BICM are compared. For a fair comparison, the code word length of the binary (component) codes are chosen such that the over{all delay is xed to 6000 transmit symbols. For N= 2 the corresponding block lengths

Abstract-- Multilevel coding and bit-interleaved coded modulation employing differential encoding and non-coherent reception over flat fading channels are assessed. In order to achieve high bandwidth efficiencies mixed amplitude/phase modulation is perform

of the binary codes are 6000 for MLC and 18000 for BICM, respectively. According to 6] in MLC the target rate 1.5 bit/ch. use pides optimally into the rates of the three component turbo{codes: R0=R1=R2= 0:17=0:53=0:80. In BICM, a single code with rate 1=2 is present. For N= 3 the block lengths of the codes are 3000 for MLC and 18000 for BICM, respectively. The rates of the six component codes in MLC are R0==R5= 0:15=0:18=0:51=0:58=0:76=0:82 (R0; R2; R4: rst transition, R1; R3; R5: second transition); the BICM code does not change. As reference, the\rate{distortion capacities" for MLC/MSD and BICM are shown. In the case of N= 2 and low Eb=N0 (bit error rates above BER= 2 10?4; Eb: average energy per information bit, N0: one{sided noise power spectral density) MLC outperforms BICM. Only for large Eb=N0 (very low error rates) BICM turns to be superior, because it takes advantage of the greater block length. Here, the error oor of the turbo codes is much lower than for the shorter codes used in MLC. For N= 3, despite the shorter codes, a clear superiority of MSD over BICM is visible. This is due to the fact, that, …… 此处隐藏：8272字，全部文档内容请下载后查看。喜欢就下载吧 ……